algebraic reading problem

Question

The measure of the first of three angles of a triangle is three times the measure of the second triangle.  The measure of the third triangle is twice the measure of the second angle.  What is the measure of each of the angles?

Answer 1

Tracy,

 

Let the 1st angle = a, the 2nd angle = , and the 3rd angle = c.  Then angle a = 3b and angle c = 2b.

 

We also know that for any triangle a + b + c = 180°

 

So substituting a = 3b and c = 2b give:  3b + b + 2b = 180°, so 6b = 180°, which means b = 30°.

 

If a = 3b, then a = 90° and c = 2b means c = 60°.  so we have a right triangle with sides of 90°, 60°, and 30°.

Answer 2

x=measure of the second angle

3x=measure of the second angle

2x=measure of the third angle

the sum of the measures of the three angles of a triangle is 180º

x+3x+2x=180

6x=180

x=180/6

x=30º

3x=90º

2x=60º

 

Answer 3

X - 2nd  measure angle

 

3X -  1st measured angle

 

2X - 3rd measured angle

 

 X + 2X + 3X = 180°

 

    6X = 180°

 

     X = 180°/ 6 = 30°  2nd measured angle

 

     2X = 2 * 30° = 60°

    

     3 X = 3 * 30° = 90°